Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19149725 | C2 | semidirect |
| 2. C22×#14583811 | C2 | semidirect |
| 3. #26012058 | C2 | semidirect |
| 4. #26011635 | C2 | semidirect |
| 5. #26011623 | C2 | semidirect |
| 6. #26011497 | C2 | semidirect |
| 7. #26011487 | C2 | semidirect |
| 8. #26011459 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C173 | C2 | semidirect |
| 12. C2×#14583827 | C22 | semidirect |
| 18. C2×D4×D173 | C22 | semidirect |
| 20. C2×#14583811 | C22 | semidirect |
| 21. C22×#13063436 | C22 | semidirect |
| 24. #19149650 | C22 | semidirect |
| 26. #19149638 | C22 | semidirect |
| 27. #19149603 | C22 | semidirect |
| 28. #19149601 | C22 | semidirect |
| 29. #19149600 | C22 | semidirect |
| 30. #19149591 | C22 | semidirect |
| 32. C22×D4×C173 | C22 | semidirect |
| 34. C2×SD16×C173 | C22 | semidirect |
| 35. C2×D8×C173 | C22 | semidirect |
| 36. C2×M16×C173 | C22 | semidirect |
| 50. C2×D692 | D4 | semidirect |
| 69. #41×C173 | D4 | semidirect |
| 151. C173 | #3008 | semidirect |
| 154. C2×AGL(1,ℤ/8) | D173 | semidirect |
| 172. C22×D4 | C2×D173 | semidirect |
| 174. C2×SD16 | C2×D173 | semidirect |
| 177. C2×D8 | C2×D173 | semidirect |
| 178. C2×M16 | C2×D173 | semidirect |
| 198. #41 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149725 | 2 |
| C22×#14583811 | 2 |
| #26012058 | 2 |
| #26011635 | 2 |
| #26011623 | 2 |
| #26011497 | 2 |
| #26011487 | 2 |
| #26011459 | 2 |
| C2×AGL(1,ℤ/8)×C173 | 2 |
| #3008 | 173 |